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In this question, we are given the sum of a certain number of terms in arithmetic progression.

Lets first understand by the term arithmetic progression.

An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant.

Also, we are given the first term of the sequence.

The first term is 5.

And the last term given is 45.

We need to know the formula for the sum of n terms.

The formula is given as follows.

$Sum=\dfrac{n}{2}\left( a+l \right)$

Where n is the number of terms,

a is the first term in the series,

l is the last term in the series.

Now, according to the condition we just have one unknown that is the number of terms.

Therefore, substituting the values a = 5, l = 45, Sum = 120,

We get,

$120=\dfrac{n}{2}\left( 5+45 \right)$

Solving the equation, we get,

$\begin{align}

& 120=\dfrac{n}{2}\left( 50 \right) \\

& n=\dfrac{120\times 2}{50} \\

& n=4.8 \\

\end{align}$